The sequence (a_n) witha_n = (((?((((((10^0)/10)+10^1)/10)+10^2)/10)+? )+10^n)/10)has the (improper) limit infinity.Here we have an improper limit that, according to analysis, hasinfinitely many digits 1 left of the decimal point (i.e., a non emptyset), and according to set theory the same limit has an empty set ofdigits left of the decimal point.>> Mückenheim is worried by the fact that for a sequence (a_n)_n of> functions a_n: Z -> {0,1} it is possible that lim_{n->oo} a_n(k)=0 for> all k while the sequence sum_{k in Z} a_n(k) * 10^k tends to infinity> for n->oo. And of course he thinks that this is somehow set theory's> fault. What idiocy!-

Sorry, you are plainly wrong. Your well-known text book example doesnot yield a contradiction between analysis and set theory. The digitsremain left of the decimal point (if there is any point at all). Onlythe positions of the digits =/= 0 cannot be determined in the limit.This is the same in analysis and set theory. And it is obviously notunder discussion here.

In order to teach you the correct argument I have explained it againabove. Every person equipped with a minimum of intelligence should beable to understand it after the second explanation. If you have notyet understood it, feel free to ask again.